Question

25 БАЛЛОВ
Решить систему, 1 пример

Answer 1

$\sqrt{14-x} >2-x\\\\1)\left \{ {{2-x<0} \atop {14-x\geq0 }} \right.\\\\\left \{ {{-x<-2} \atop {-x\geq-14 }} \right.\\\\\left \{ {{x>2} \atop {x\leq 14}} \right.$

x ∈ (2 , 14]

$2)\left \{ {{2-x\geq0 } \atop {14-x>(2-x)^{2} }} \right. \\\\\left \{ {{-x\geq-2 } \atop {14-x>4-4x+x^{2} }} \right.\\\\\left \{ {{x\leq2 } \atop {-x^{2}+4x-4+14-x>0 }} \right.\\\\\left \{ {{x\leq 2} \atop {x^{2}-3x-10<0 }} \right.\\\\\left \{ {{x\leq2 } \atop {(x-5)(x+2)<0}} \right.$

       +                       -                        +

________(-2)_________(5)____________

                  |||||||||||||||||||||||||||||||||

_______________[2]______________

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

x ∈ (-2 ; 2]

Ответ : x ∈ (- 2 ; 14]